For the purpose of improving the fastness of dyes or prints on textile material, it is customary to effect an after-treatment, usually designated "soaping", following the dyeing or printing process. Alkaline salts, such as sodium carbonate, are frequently used for this soaping process in addition to anionic and/or nonionic surface-active compounds or tensides. Loosely adhering dye is thereby either washed out by the soap from the fiber or it is more strongly fixed, thus leading to an increase in the washing fastness and rubbing fastness of the dyed textile material. This increased fixing of the dye arises from the agglomeration of individual molecules of dye to form molecular associations. Substances such as carboxymethyl cellulose or builders, such as are used in washing agents, do not improve the fastness of the dyes, or do not improve it to an adequate extent. In contrast to conventional domestic washing methods, the processing waters used in the textile industry, that is in the dyeing baths, rinsing and soaping liquors, are usually pre-softened.